Adding Polynomials
Subtracting Polynomials
Multiplying and Dividing Polynomials
Key Features
Zeros of Polynomials
Naming Polynomials
100
Add the Polynomials
(4x + 9) +(x - 4)
5x + 5
100
Subtract the polynomials:
(g - 4) - (3g - 6)
-2g + 2
100
Multiply the Polynomials:
3x2 (2x4)
6x6
100
Complete the end behavior of the polynomial listed below: (NO DESMOS)
f(x)=-3x^4+5x^3
As x -> ____, f(x) ->_____
As x -> ____, f(x) ->_____
Infinity, -infinity
-Infinity, -infinity
100
List the zeros of the function and their multiplicity
f(x)=(x-1)^2(x+2)
1 (multiplicity 2),-2
100
3x+5
Linear Binomial
200
Add the polynomials:
(-3a - 2) + (7a + 5)
4a + 3
200
Subtract the polynomials:
(-5h - 2) - (7h +6)
-12h - 8
200
Multiply the Polynomials:
2x(x + 5)
2x^2 + 10x
200
Complete the end behavior of the polynomial listed below: (NO DESMOS)
f(x)=-x^3-3x^2+2
As x -> ____, f(x) ->_____
As x -> ____, f(x) ->_____
Infinity, -infinity
-Infinity, infinity
200
If 1 is a zero of the polynomial listed below, what are the other two zeros?
f(x)=(2x-1)(x+3)(x-1)
x=1/2, -3
200
3x3+12x+1
Cubic Trinomial
300
Add the polynomials:
(x2 +3x + 5) + ( -x2 +6x)
9x + 5
300
Subtract the polynomials:
(-x2 - 5) - (-3x2 -x -8)
2x2 + x +3
300
Multiply the Polynomials:
(2x + 3)(x + 1)
2x^2 + 5x + 3
300
Complete the end behavior of the polynomial listed below: (NO DESMOS)
f(x)=67x^1002-67x^67+67x^76+67
As x -> ____, f(x) ->_____
As x -> ____, f(x) ->_____
Infinity, infinity
-Infinity, infinity
300
How many zeros does the polynomial have, including imaginary roots and repeated roots?
f(x)=8x^6+65x^3+8
6
300
4x^2
Quadratic Monomial
400
Add the polynomials:
(t2 + 3t3 -3) + (2t2 +7t -2t3)
t3 +3t2 +7t -3
400
Subtract the Polynomials:
(k2 + 6k3 -4) - (5k3 + 7k -3k2)
k3 + 4k2 -7k -4
400
Multiply the Polynomials:
(y + 5)(y2 + 2y - 6)
y^3 + 7y^2 + 4y - 30
400
What are the zeros and their multiplicities?
-2 (multiplicity 1), 0 (multiplicity 2), 2 (multiplicity 1)
400
Write a polynomial function of the least degree with the given zeros and their multiplicity
2, 3 (multiplicity 3), -1 (multiplicity 5)
y=(x-2)(x-3)^3(x+1)
400
8x5+x4+4x3-2x+1
Quintic Polynomial
500
Add the polynomials:
(-1 + x2 + 2x) + (1 -2x + 2x2)
3x2
500
Subtract the Polynomials:
(2x - 3x) - (x2 -2x + 4)
-x2 + x - 4
500
Divide the Polynomials:
(12x5 - 16x4 + 8x3 - 20x2) / (4x)
3x4 - 4x3 + 2x2 - 5x
500
What are the relative extrema of this function (list the points, round to the nearest integer)?
Max: (-1, 4), (4, 0)
Min: (-3, -5), (2, -2)
500
Write a polynomial function of the fourth degree with the given zeros.
-1, 3, 2, 8
f(x)=(x+1)(x-3)(x-2)(x-8)
500
2x^4 +3x-4
Quartic Trinomial
600
Add the polynomials:
(2x2 + 6y + 3xy) + (3x2 - 5xy - x)
5x2 - 2xy - x + 6y
600
Subtract the following polynomials
(3 - 6x5 - 8x4) - (-6x4 - 3x - 8x5)
2x5 - 2x4 + 3x + 3
600
Divide the Polynomials:
(7x3 - 28x2 - 49x) / (7x)
x2 - 4x - 7
600
What is the number of zeros of the polynomial? Number of turning points?
3 zeros and 2 turning points
600
Factor and solve to find all the zeros of the polynomial
f(x)=x^4-13x^2+36
x=2, -2, 3, -3
600
-4x^2-3x+5x^5-7
Quintic Polynomial